Dealers do not reject claims. They make a large portion of their income from claims. The manufacture rejects claims. if you use the dealer for service they have records of that and so can sometimes prove that the relavent maitenance was done correctly but they want the money from warranty work either way and so they lose if the claim is rejected.

they make money from regular service as well and want you for that. However warranty work is too valuable to them to ignore

Yes, but like I said in my other comment - the manufacturer will reject any claim for a car that doesn't have a full service history within their own dealer network. The manufacturer will allow the dealer to submit other proof that the car has been serviced properly, but that takes time and effort, which the dealers don't want to spare, so they decline your warranty claim by not putting it in front of the manufacturer(because that would mean more work for them).

Manufactures are not that bad. They know the law and so they won't ask for maintenance records unless that could be relevant. Many claims are rejected though because the wrong chemical (oil, coolant...) will cause failures which they know the symptoms - that is why they require specific records - they know that issues of a specific nature are often caused by not following maintenance schedules.

Of course it is in the manufactures interest to reject claims where they can. However it is also in their interest to pay out for claims since ease of handling issues is what builds loyalty.